1. This is the Supreme Court of the USA.
2. These are the Supreme Courts of the USA.
3. This is the supreme court of the USA.
(Which one is correct? Do I have to capitalize? Do you have only one supreme court? Or do you have many supreme courts?)
4. the Supreme Court > a high court > a district court
(Are they correct?)
#1 is correct. There is only one for the country.
I don't understand what you're signifying in #4. Please explain.
1. The correct sentence is "This is the Supreme Court of the USA." In this sentence, "Supreme Court" should be capitalized because it is the specific name of the highest court in the United States.
2. The sentence "These are the Supreme Courts of the USA" is incorrect. There is only one Supreme Court in the United States, so the plural form "Supreme Courts" is inappropriate.
3. The sentence "This is the supreme court of the USA" is technically correct, but it should still be capitalized as "Supreme Court" since it is a proper noun and the official name of the highest court in the country.
4. The sentence "the Supreme Court > a high court > a district court" is a hierarchy that correctly depicts the judicial structure in the United States. The Supreme Court is the highest court, followed by the various high courts (also known as appellate courts), and then the district courts, which are the lower trial courts.